Abstract
The problem of computing bounds on the region-of-attraction for systems with polynomial vector fields is considered. Invariant subsets of the region-of-attraction are characterized as sublevel sets of Lyapunov functions. Finite-dimensional polynomial parametrizations for Lyapunov functions are used. A methodology utilizing information from simulations to generate Lyapunov function candidates satisfying necessary conditions for bilinear constraints is proposed. The suitability of Lyapunov function candidates is assessed solving linear sum-of-squares optimization problems. Qualified candidates are used to compute invariant subsets of the region-of-attraction and to initialize various bilinear search strategies for further optimization. We illustrate the method on small examples from the literature and several control oriented systems.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 2669-2675 |
| Number of pages | 7 |
| Journal | Automatica |
| Volume | 44 |
| Issue number | 10 |
| DOIs | |
| State | Published - Oct 1 2008 |
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Keywords
- Local stability
- Nonlinear dynamics
- Region-of-attraction
- Simulations
- Sum-of-squares programming
Cite this
Local stability analysis using simulations and sum-of-squares programming. / Topcu, Ufuk; Packard, Andrew; Seiler, Peter.
In: Automatica, Vol. 44, No. 10, 01.10.2008, p. 2669-2675.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Local stability analysis using simulations and sum-of-squares programming
AU - Topcu, Ufuk
AU - Packard, Andrew
AU - Seiler, Peter
PY - 2008/10/1
Y1 - 2008/10/1
N2 - The problem of computing bounds on the region-of-attraction for systems with polynomial vector fields is considered. Invariant subsets of the region-of-attraction are characterized as sublevel sets of Lyapunov functions. Finite-dimensional polynomial parametrizations for Lyapunov functions are used. A methodology utilizing information from simulations to generate Lyapunov function candidates satisfying necessary conditions for bilinear constraints is proposed. The suitability of Lyapunov function candidates is assessed solving linear sum-of-squares optimization problems. Qualified candidates are used to compute invariant subsets of the region-of-attraction and to initialize various bilinear search strategies for further optimization. We illustrate the method on small examples from the literature and several control oriented systems.
AB - The problem of computing bounds on the region-of-attraction for systems with polynomial vector fields is considered. Invariant subsets of the region-of-attraction are characterized as sublevel sets of Lyapunov functions. Finite-dimensional polynomial parametrizations for Lyapunov functions are used. A methodology utilizing information from simulations to generate Lyapunov function candidates satisfying necessary conditions for bilinear constraints is proposed. The suitability of Lyapunov function candidates is assessed solving linear sum-of-squares optimization problems. Qualified candidates are used to compute invariant subsets of the region-of-attraction and to initialize various bilinear search strategies for further optimization. We illustrate the method on small examples from the literature and several control oriented systems.
KW - Local stability
KW - Nonlinear dynamics
KW - Region-of-attraction
KW - Simulations
KW - Sum-of-squares programming
UR - http://www.scopus.com/inward/record.url?scp=52949089284&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=52949089284&partnerID=8YFLogxK
U2 - 10.1016/j.automatica.2008.03.010
DO - 10.1016/j.automatica.2008.03.010
M3 - Article
VL - 44
SP - 2669
EP - 2675
JO - Automatica
JF - Automatica
SN - 0005-1098
IS - 10
ER -